Difference between push/pull and shrink/fatten?
They don't actually do the same things.


Shrink/Fatten scales the selected elements along their normals.



I've enabled face normals display in the above gif so that you can see that each face is moving along it's normal (blue lines).
Push/Pull moves the selected elements farther/closer to the pivot point.



Here you can see that the faces are not moving along their normals, but instead are moving away from/closer to the pivot point. In this case, the pivot is the median location of the selected elements, which happens to be the world center in this particular example.